It is a sound principle in teaching that we should begin by saying what a thing is, rather than what it is not, but the reader of the Gazette is not coming across the word involution for the first time, anti the best serrice I can render him is to insist at the outset that involution is not a form of homography Before I can enlarge on this warning, I must add another. In elementary work we are in no danger of confusing the relation of collinearity, a relation between three or more points, with a class of collinear points, for which we have the familiar name of line. But the one word involution has been made to do duty both for a relation and for a class, and although when we understand the subject we can always interpret the word froin the context, the teacher will find it worth while to sacrifice brevity for a time and to tallr of the involution-relation and of an involution-class.